A373665 - OEIS

%I #7 Jun 13 2024 01:44:10

%S 10,11,14,15,23,26,27,35,38,39,45,50,59,62,68,71,74,83,86,95,98,102,

%T 103,107,110,114,115,119,122,131,134,137,138,139,143,155,158,159,164,

%U 167,170,174,179,182,183,186,190,191,194,202,203,206,215,219,227,230

%N Positive integers that cannot be written as a sum of a practical number and a 16-gonal number.

%C Somu and Tran (2024) proved that there are infinitely many such integers. More generally, infinitely many positive integers cannot be written as a sum of a practical number and an s-gonal number if s is congruent to 4 modulo 12.

%H Duc Van Khanh Tran, <a href="/A373665/b373665.txt">Table of n, a(n) for n = 1..10000</a>

%H Sai Teja Somu and Duc Van Khanh Tran, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Somu/somu5.html">On sums of practical numbers and polygonal numbers</a>, Journal of Integer Sequences, 27(5), 2024.

%Y Cf. A005153, A051868.

%K nonn

%O 1,1

%A _Duc Van Khanh Tran_, Jun 12 2024